There has been and are significant scientific and engineering efforts under way to develop energy storage devices which can store larger amounts of electrical energy within specifications of lower weights and smaller volumes than can be purchased today in the world wide market place. The United States Department of Energy has set target goals for electric vehicle batteries with the specifications of 100 watt-hours per kilogram, 200 watt-hours per liter at a cost of $500 per kilowatt-hour in 2012 and 200 watt-hours per kilogram, 400 watt hours at a cost of $125 per kilowatt-hour in 2022. Capacitors are also known for their fast charging abilities, safe operations, long life cycles and for high power densities, but to this date they lack the abilities to store large amounts of electrical energy in small volumes and with low weights in a high density capacitor. The problem with all the well known electrical energy storage approaches is the realization of the mass production means and methods needed to deliver an electrical energy storage devise with low weight, low volume, at a low enough cost, and long enough life cycle to be able to achieve an initial $500 per kilowatt hour marketing price today, and the lack the ability to reduce this initial price to $125 per kilowatt hour of electrical energy storage in the succeeding generations of product realizations by 2022.
Capacitance is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits some capacitance. A common form of energy storage device is a parallel-plate capacitor. In a parallel plate capacitor, capacitance is directly proportional to the surface area of the over lapping portions of the positive and negative plates, and inversely proportional to the separation distance between the plates and the relative permittivity of the material or lack of material between the over lapping portions of the positively charged and negatively charged plates. If the charges on the plates are +q and −q, and V gives the voltage between the plates, then the capacitance C is given by:C=q/V.  (Equation one)which gives the voltage/current relationship:I(t)=C dV(t)/dt.  (Equation Two)where C=capacitance; q=charge; V=volts; I=current and t=time.
The capacitance is a function of the physical dimensions of the overlapping area of the positive and negative electrodes and the dielectric thickness between the electrodes along with the permittivity constant of the dielectric material also known as the dielectric constant of the insulating material. The capacitance is independent of the potential difference between the conductors and the total charge on them. The SI unit of capacitance is the farad (symbol: F), named after the English physicist Michael Faraday, a 1 farad capacitor when charged with 1 coulomb of electrical charge will have a potential difference of 1 volt between the positive and negative plates. Historically, a farad was regarded as an inconveniently large unit, both electrically and physically. Its subdivisions were invariably used, namely the microfarad, nanofarad and picofarad. More recently, technology has advanced such that capacitors of 1 farad and greater can be constructed in a structure little larger than a coin battery (so-called supercapacitors). Such capacitors are principally used for energy storage replacing more traditional batteries. The energy (measured in joules) stored in a capacitor is equal to the work done to charge it. A capacitor of capacitance C, holding a charge +q on one plate and −q on the other. Moving a small element of charge dq from one plate to the other against the potential difference V=q/C requires the work dW:dW=q/C dq  (Equation Three)where W is the work measured in joules, q is the charge measured in coulombs and C is the capacitance, measured in farads.
The energy stored in a capacitor is found by integrating this equation. Starting with an uncharged capacitance (q=0) and moving charge from one plate to the other until the plates have charge +Q and −Q requires the work W:Wcharging=0.5(Q2/C)=0.5 QV=0.5 CV2=Wstored  (Equation Four)The capacitance of the majority of capacitors used in electronic circuits is generally several orders of magnitude smaller than the farad. The most common subunits of capacitance in use today are the microfarad (mF), nanofarad (nF), picofarad (pF), and, in microcircuits, femtofarad (fF).Capacitance can be calculated if the geometry of the conductors and the dielectric properties of the insulator between the conductors are known. For example, the capacitance of a parallel-plate capacitor constructed of two parallel plates both of area A separated by a distance d is approximately equal to the following:C=εrε0(A/d)  (Equation Five)where C is the capacitance, in Farads; A is the area of overlap of the two plates, in square meters; εr is the relative static permittivity (sometimes called the dielectric constant) of the material between the plates (for a vacuum, εr=1); ε0 is the electric constant, the permittivity of free space (ε0≃8.854×10−12 F m−1) and d is the separation between the plates, in meters. The equation is a good approximation if d is small compared to the other dimensions of the plates so the field in the capacitor over most of its area is uniform, and the so-called fringing field around the periphery provides a small contribution.
The energy stored in a capacitor, for a flat-plate capacitor the energy stored is:Wstored=0.5(CV2)=0.5 εrε0(A/d)V2  (Equation Six)where W is the energy, in joules; C is the capacitance, in farads; and V is the voltage, in volts.